DIVISION – STAGE 1
Solve problems
including halving and
sharing.
Practical Sharing
I have 6 sweets to share between 2 plates. How many on each?
Count repeated groups
of the same size by
counting on and back in
1s, 2s, 5s and 10s
Following the
pattern of ’one for
me, one for you’
Begin to use vocabulary
associated with
division.
Practical pairing
Record using marks,
which they can
interpret and explain.
Children will also be encouraged to join in with practical halving problems eg: chopping a chocolate bar with
squares up, or sharing out orange segments.
half, halve, pair, count out, share out, left, left over
DIVISION – STAGE 2
Practical Sharing
I have 20 chocolate buttons. I want to share them between 5 children. How many do they get each?
Solve one-step
practical problems that
involve sharing into
equal groups including
2, 5 or 10. Problems
to include objects,
shapes, quantities and
measures.
Find a half and quarter
of simple quantities, up
to 20, as one of two
or four equal parts.
Following the pattern of
’one for me, one for you’
Children may begin to make marks to represent moving each object.
x
x
x
x
x
Practical grouping
Star stickers come in packs of 5. How many packs will I have with 15 stickers?
Children count 1, 2,3,4,5 and then circle/gather each group.
Arrays
X X X X X
X X X X X
X X X X X
1
2
3
15 grouped into 5s gives us 3 groups
Division as halving/sharing
We split a cake in half(quarters), we have 8 Smarties.
How many need to go on each halve to be fair/equal?
half, halve, pair, count out, share out, left, left over, = equals, sign, is the same as
DIVISION – STAGE 3
Represent sharing grouping as
division
Use practical and informal
written methods and related
vocabulary and notation to
support division including
calculations with remainders.
Use symbols ÷ and = to record
and interpret number sentences
Known facts – Children should begin to recall division facts for the 2, 5 and 10 tables. Counting in steps.
Sharing (practical and recording)
20 shared into 5s.
Grouping (practical and recording)
20 grouped into 5s.
A goldfish bowl can hold 5 fish. How many bowls do we need for 23 fish?
1 lot
2 lots
3 lots
4 lots
3 remaining
Solve number sentences with
missing numbers
Understand the order in which
division is done impacts on the
answer.
Recognise and use the inverse
relationship between x and ÷
Solve problems in a variety of
contexts including using £ OR
p.
Understand 1/3 as sharing
between 3 equal groups.
0
5
10
15
20
23 ÷ 5 = 4 bowls 3, You would need 5 bowls for the fish.
23
Using Arrays (grouping)
How many 4s go into 20?
Using Thirds eg:
I have 9 smarties, I give 1/3 to my friend. How many does she get?
Solving Problems
Children will be expected to use the strategies above to solve:
§ Word problems eg: I have £8 to share with me and my 3 friends, how much do we get each?
§ Missing number problems eg: 16÷__ = 8
half, halve, pair, count out, share out, left, left over, =, equals, sign, is the same as, lots of, groups of,
repeated addition, array, row, column, share equally, one each, two each, three each…, group in pairs, threes…
tens, equal groups of, ÷, divide, divided by, divided into
DIVISION – STAGE 4
Use tables to solve problems
related to 2, 3, 4, 5, 8 and
10.
Known facts – Children will be expected to recall division facts for the 2, 3, 4, 5, 8 and 10 tables. They
should counting in steps for non-known tables.
Arrays
Target Division
Use practical and informal
written methods to divide
two-digit numbers (e.g. 60 ÷
4); round remainders up or
down, depending on the
context.
Understand that division is
the inverse of multiplication
and vice versa; use this to
derive and record related
multiplication and division
number sentences.
Find unit fractions of numbers
and quantities (e.g. 1/2 , ¼,
1/3 and 1/6 or 1/10 of a
small unit of sweets). Also
non-unit fractions such as 2/4
and ¾.
Solving Problems
Children will be expected to use the strategies above to solve:
§
Word problems eg: I have 12 smarties, I take 1/4 for myself. How many do I get? I have 40
stickers, they need to be packed into packets of 8. How many packets will we have?
§ Missing number problems eg: 24 ÷ __ = 3
half, halve, pair, count out, share out, left, left over, =, equals, sign, is the same as, lots of, groups of,
repeated addition, array, row, column, share equally, one each, two each, three each…, group in pairs,
threes… tens, equal groups of, ÷, divide, divided by, divided into
Multiply and divide numbers to
1000 by 10 and then 100
(whole number answers)
understanding the effect;
relate to scaling up or down.
DIVISION – STAGE 5
Known facts – Children should be able to recall division facts from 1 x 1 to 10 x 10 tables.
Target division
Know what happens when you
divide by 1.
Develop and use written
methods to record, support and
explain multiplication and
division of two-digit numbers
by a one-digit number,
including division with
remainders (e.g. 99 ÷ 6)
Find unit fractions and nonfractions of numbers, where
the answer is a whole number.
Solving Problems
Children will be expected to use the strategies above to solve:
§
Word problems eg: I have 12 smarties, I take 3/4 for myself. How many do I get? I have 40
stickers, they need to be packed into packets of 8. How many packets will we have?
§
Missing number problems eg: 56 ÷ __ = 8
half, halve, pair, =, equals, sign, is the same as, lots of, groups of, share equally, one each, two each, three each…, group
in pairs, threes… tens, equal groups of, ÷, divide, divided by, divided into, remainder, factor, quotient, divisible by,
inverse
DIVISION – STAGE 6
Use understanding of
Known facts – Children should recall division facts using 1 x 1 to 12 x 12 tables.
place value to multiply
and divide whole numbers Target Division
and decimals 10, 100 and
1000. (connect with
converting kg and g etc)
Refine and use efficient
written methods to
multiply and divide
ThHTU ÷ U
Find fractions using
division (e.g. 1/100 of 6
kg)
Express remainders as
fractions or decimals
Showing answers as fractions, decimals and remainders as required
231 ÷ 5 = 46.2
= 46 1/5
= 46 r 1
Solving Problems
Children will be expected to use the strategies above to solve word problems and missing number problems.
half, halve, pair, =, equals, sign, is the same as, lots of, groups of, share equally, one each, two each, three each…, group in pairs, threes…
tens, equal groups of, ÷, divide, divided by, divided into, remainder, factor, quotient, divisible by, inverse
DIVISION – STAGE 7
Use efficient written
methods to
• Divide a ThHTU
by TU
• divide integers
and decimals by a
one-digit integer.
Known facts – Children should recall division facts using 1 x 1 to 12 x 12 tables.
Target Division
Target Division with decimals
Express a quotient as a
fraction or decimal (e.g.
67÷5=13.4 or 13 2/5)
Divide proper fractions
by whole numbers. E.g.
1/3 by 2.
Relate fractions to
multiplication and division
(e.g. 6 ÷ 2 = ½ of 6 = 6
x ½),
Compact Division
243 ÷ 9 = 27
Divide proper fractions by whole numbers
Children will learn practically first – e.g. Using a diagram
of 1/3 then divide it into 2 equal bits – what happens?
It becomes one sixth.
0 2 7
9 2 4 3
0 0 0
1 8 0
6 3
How many 90 0 (hundreds) go into
this number?
How man y 90 s (tens) go into the
remainder of this number?
How man y 9s (units) go into the
remainder of this number?
Introduction to 1/3 ÷ 2 = 1/3 ÷ 2/1 = 1/3 x ½ (linking
with multiplying fractions)
Solving Problems
Children will be expected to use the strategies above to solve word problems and missing number problems.
half, halve, pair, =, equals, sign, is the same as, lots of, groups of, share equally, one each, two each, three each…, group in pairs, threes…
tens, equal groups of, ÷, divide, divided by, divided into, remainder, factor, quotient, divisible by, inverse